We study the single-particle dynamics in a general and parameterized alternating-gradient cell with zero chromaticity using the Lie Algebra method. To our surprise, the first-order perturbation of the sextupoles largely determines the dynamics away from the major resonances. The dynamic aperture can be estimated from the topology and geometry of the phase space. In the linearly normalized phase space, it is scaled according to, $\bar A \propto \phi\sqrt{L}$, where $\phi$ is the bending angle and $L$ the length of the cell. For the two degrees of freedom with equal betatron tunes, the analytical perturbation theory leads us to the invariant or quasi-invariant tori, which play an important role in determining the stable volume in the four-dimensional phase space. Show Partial Abstract